We present a classical algorithm for simulating universal quantum circuits composed of "free" nearest-neighbour matchgates or equivalently fermionic-linear-optical (FLO) gates, and "resourceful" non-Gaussian gates. We achieve the promotion of the efficiently simulable FLO subtheory to universal quantum computation by gadgetizing controlled phase gates with arbitrary phases employing non-Gaussian resource states. Our key contribution is the development of a novel phase-sensitive algorithm for simulating FLO circuits. This allows us to decompose the resource states arising from gadgetization into free states at the level of statevectors rather than density matrices. The runtime cost of our algorithm for estimating the Born-rule probability of a given quantum circuit scales polynomially in all circuit parameters, except for a linear dependence on the newly introduced FLO $extent$, which scales exponentially with the number of controlled-phase gates. More precisely, as a result of finding optimal decompositions of relevant resource states, the runtime doubles for every maximally resourceful (e.g., swap or CZ) gate added. Crucially, this cost compares very favourably with the best known prior algorithm, where each swap gate increases the simulation cost by a factor of approximately 9. For a quantum circuit containing arbitrary FLO unitaries and $k$ controlled-Z gates, we obtain an exponential improvement $O(4.5^k)$ over the prior state-of-the-art.

中文翻译：

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改进了以自由费米子操作为主的量子电路的模拟


我们提出了一种经典算法，用于模拟由“自由”最近邻匹配门或等效的费米子线性光学 （FLO） 门和“足智多谋”的非高斯门组成的通用量子电路。我们通过将具有采用非高斯资源状态的任意相位的受控相门化，实现了将可高效模拟的 FLO 子论推广为通用量子计算。我们的主要贡献是开发了一种用于模拟 FLO 电路的新型相位敏感算法。这允许我们将小工具化产生的资源状态分解为状态向量而不是密度矩阵级别的自由状态。我们用于估计给定量子电路的 Born 规则概率的算法的运行时间成本在所有电路参数中都呈多项式缩放，除了对新引入的 FLO $extent$ 的线性依赖性，它随受控相位门的数量呈指数级缩放。更准确地说，由于找到相关资源状态的最佳分解，每添加一个最大资源（例如，swap 或 CZ）门，运行时间就会加倍。至关重要的是，与最著名的先前算法相比，这个成本非常有利，在以前的算法中，每个交换门都会使仿真成本增加大约 9 倍。对于包含任意 FLO 幺正和 $k$ 受控 Z 门的量子电路，我们获得了比先前最先进的 $O（4.5^k）$ 的指数级改进。